Question: Rewrite the expression in the form $x^n$. $\sqrt{x^{^{\scriptsize\dfrac34}}x^{-1}}=$
Solution: $\begin{aligned} \sqrt{x^{^{\scriptsize\dfrac34}}x^{-1}}&=\sqrt{x^{^{\scriptsize\dfrac34 -1}}} \\\\ &=\sqrt{x^{^{\scriptsize -\dfrac14}}} \\\\ &=\left(x^{^{\scriptsize -\dfrac14}}\right)^{^{\scriptsize\dfrac12}} \\\\ &=x^{^{\scriptsize -\dfrac14\cdot\dfrac12}} \\\\ &=x^{^{\scriptsize -\dfrac18}} \end{aligned}$